Fluidization of granular media wetted by liquid ${}^4\mathrm{He}$

We explore experimentally the fluidization of vertically agitated polymethylmethacrylate spheres wetted by liquid ${}^4\mathrm{He}$. By controlling the temperature around the $\lambda$ point, we change the properties of the wetting liquid from a normal fluid (helium I) to a superfluid (helium II). For wetting by helium I, the critical acceleration for fluidization $\left({\Gamma }_c\right)$ shows a steep increase close to the saturation of the vapor pressure in the sample cell. For helium II wetting, ${\Gamma }_c$ starts to increase at about 75% saturation, indicating that capillary bridges are enhanced by the superflow of the unsaturated helium film. Above saturation, ${\Gamma }_c$ enters a plateau regime where the capillary force between particles is independent of the bridge volume. The plateau value is found to vary with temperature and shows a peak at $2.1\mathrm{K}$, which we attribute to the influence of the specific heat of liquid helium.

Figure 1

(Color online) Sketch of the experimental setup. (a) is a typical top view of the sample. The temperature in the cryostat (b) is adjusted by controlling the pressure [measured by pressure gauge (c)] above the liquid helium. Helium gas is added into the sample chamber through a capillary (d). Gauge (e) measures the pressure difference between cell and cryostat. The sample is illuminated by laser pulses, and images are taken by a charge-coupled device camera (f) with a polarizer (g) in front. The sample cell can be vibrated vertically by an electrodynamic shaker (LDS V555) which is mounted upside down above the cryostat. The strength of vibration is measured by an accelerometer (PCB Piezotronics 353B33) (i).

Figure 2

(Color online) Scaled critical acceleration for fluidization, ${\Gamma }^{*}$, as a function of the amount of helium added, $n^{*}$, for superfluid (top) and normal fluid (bottom) wetting. ${\Gamma }^{*}=0$ corresponds to the behavior of dry grains, and $n^{*}=1$ to the transition from an unsaturated to a saturated helium film. Three different regimes can be distinguished: dry (1), asperity (roughness) (2), and complete wetting (3). Sketches of the three regimes on the grain size scale are shown in the middle. The dashed lines separating the regimes are guides to the eye. Each data point is an average of three measurements; the standard error is within 0.05.

Figure 3

(Color online) (a) In regime 2 ${\Gamma }^{*}$ varies linearly with the scaled saturation ${[-\ln \left(n^{*}\right)]}^{-1∕3}$. Dotted lines are fits with Eq. (3). The inset of (a) shows the temperature dependence of the fit parameter $k_c$. (b) The temperature dependence of the plateau value of ${\Gamma }^{*}$ in regime 3 (black dots). The dark green line is the specific heat $C_s$ of bulk helium taken from [38]. The inset of (b) shows a sketch of two completely wetted particles. The color code illustrates the temperature gradients generated by energy dissipation. Blue dashed arrows indicate the flow of superfluid in the helium film driven by the fountain effect, and blue dotted arrows depict evaporation of helium from the surface of the meniscus.